Because deduction involves starting with a general theory and making more specific predictions from that, I would first identify the theory. In this case the theory is that extraterrestrial aliens visited Earth thousands of years ago and introduced scientific innovations to the human race. Next, I would look for evidence of this theory and investigate its scientific validity. For example, the Baghdad Battery could be one of those pieces of possible evidence, and I would investigate its probable uses and cultural meaning. It’s important to look at the context in which the artifact was found, and what other archaeological evidence we have of its usage to determine how it was introduced and used.
One case that was outlined in Ancient Aliens is the Dendera Light Bulb. In the show, they claim that one of the pictures on the walls of the Dendera complex shows a light bulb, indicated by the shape. However, Egyptian historians understand very well that the image in question actually has a lotus flower with their aroma depicted coming out of them. There is also a snake represented inside the “light bulb” and a djed column under it. These three items are actually common in Egyptian mythology. The lotus flower is a symbol for the sun and creation, the djed column is a symbol for stability, and the snake coming out of the lotus represents fertility, as the god Atum, the creator, is associated with snakes. One only needs to look at the cultural context in which these images exist. In fact, it’s imperative that you do so, because nothing really makes sense out of context, or at the very least, it can be misconstrued, as is the case with the explanation from Ancient Aliens. Plus, all of this information was easily attainable, from sources who are much more knowledgeable in the topic than I am, and therefore have a better grasp on what’s actually being represented.